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The technique of Darboux transformation is applied to nonlocal partner oftwo-dimensional periodic A_{n-1} Toda lattice. This system is shown to admit arepresentation as the compatibility conditions of direct and dualoverdetermined linear systems with quantized spectral parameter. Thegeneralization of the Darboux transformation technique on linear equations ofsuch a kind is given. The connections between the solutions of overdeterminedlinear systems and their expansions in series at singular points neighborhoodare presented. The solutions of the nonlocal Toda lattice and infinitehierarchies of the infinitesimal symmetries and conservation laws are obtained.Comment: 12 pages, infinitesimal symmetries and conservation laws are adde

Darboux transformations, infinitesimal symmetries and conservation laws for the nonlocal two-dimensional Toda lattice